Rigify not generating a full rig skeleton
Rigify uses a python script to generate the controller rig. Changes to the base metarig can mess up this script, preventing parts of the armature being generated.

While it looks like you started with the metarig, your rig doesn't have a spine or shoulder bones. The original metarig has hips-spine-chest-shoulder-upper_arm you have hips-chest-upper_arm. These missing bones will be the reason the script is failing.

Create a new metarig and adjust the existing bone positions to where you want them, leaving each existing bone in place.